Formula & Calculator
Historical Volatility (Annualized)
Converts daily price volatility into an annualized figure, standard practice for comparing volatility across assets and timeframes.
Interpretation
σ_annual = σ_daily × √(365). Annualised volatility from daily returns. Used to measure price variability and to set option prices.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| σ_annual | Annualized volatility | % |
| σ_daily | Daily standard deviation of returns | % |
What it means
Historical volatility is the standard deviation of returns over a period. Annualising daily volatility assumes independence and is used to compare volatility across different time frames. This is used in risk management and in option pricing. Understanding volatility is essential for traders and investors to assess market conditions and to set position sizes. High volatility indicates greater risk.
Worked example
Historical Volatility – Two Detailed Examples
Real‑World| Parameter | Value |
|---|---|
| Daily Volatility (%) | 3.5 |
| Parameter | Value |
|---|---|
| Daily Volatility | 2.0% |
Common mistakes
- Annualised volatility: σ_annual = σ_daily × √(365) (or √(252) for trading days).
- σ_daily: Standard deviation of daily returns.
- √365: Assumes calendar days – use √252 for business days.
- Volatility: A key input for risk models.
Applications
Historical volatility (annualized) converts daily volatility to an annualised figure, scaling by the square root of trading days. This is used to measure the price fluctuation of an asset. Investors and traders use it to gauge risk, to price options, and to set position sizes. Higher volatility indicates greater uncertainty. Understanding historical volatility is essential for risk management and for derivatives pricing.
- Measuring the risk and uncertainty of an asset
- Setting position sizes and stop‑loss levels
- Option pricing and implied volatility comparison
- Assessing market sentiment and regime
- Educational understanding of volatility
Frequently Asked Questions
σ_annual = σ_daily × √365. First, calculate the standard deviation of daily returns over a period (e.g., 30, 90, or 365 days), then multiply by the square root of the number of trading days in a year (365 for crypto, 252 for stocks).
Annualised volatility is a key input in options pricing models (like Black-Scholes). It also helps investors gauge the expected range of price movements over a year, which is essential for risk budgeting.
Historical volatility is based on past price data. Implied volatility is derived from option prices and reflects the market's expectation of future volatility. They often differ.
A shorter period (e.g., 30 days) captures recent volatility and is more responsive to current market conditions. A longer period (e.g., 365 days) smooths out short-term spikes and gives a more stable measure.
Yes, you can estimate that price will stay within approximately ±1σ from the mean with 68% probability, and ±2σ with 95% probability, assuming a normal distribution.
Bitcoin typically has annualized volatility around 50-80%, while altcoins can be even higher (100-200%). This is much higher than traditional assets.
Higher volatility requires wider stop-losses to avoid being stopped out by normal price fluctuations. You can adjust stop-loss distance based on the asset's ATR or historical volatility.
Often, volatility increases during downtrends (fear) and can be lower during steady uptrends. However, crypto markets can be volatile in both directions.